We study neutrino-induced charged-current (CC) π0 production on carbon nuclei using events with fully imaged final-state proton-π0 systems. Novel use of final-state correlations based on transverse kinematic imbalance enables the first measurements of the struck nucleon’s Fermi motion, of the intranuclear momentum transfer (IMT) dynamics, and of the final-state hadronic momentum configuration in neutrino pion production. Event distributions are presented for (i) the momenta of neutrino-struck neutrons below the Fermi surface, (ii) the direction of missing transverse momentum characterizing the strength of IMT, and (iii) proton-pion momentum imbalance with respect to the lepton scattering plane. The observed Fermi motion and IMT strength are compared to the previous MINERνA measurement of neutrino CC quasielastic-like production. The measured shapes and absolute rates of these distributions, as well as the cross section asymmetries, show tensions with predictions from current neutrino generator models.1 MoreReceived 13 February 2020Accepted 28 September 2020Corrected 11 December 2020DOI:https://doi.org/10.1103/PhysRevD.102.072007Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNeutrino interactionsNucleus-neutrino interactionsParticle interactionsParticles & Fields